Finite Group Databasebeta

← Group #349036

Character table — Group #349036

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222224444444444444444444444488888888888888888161616161616161632323232
order12222244444488882244444444488888888888844444444888888888888888882288
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111-1-1-1-1111111111-1-1-1-111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-1111111111-1-1-1-1111111-1-111-1-1-1-11-1-111-1-1-1-11111-1-1-1-111-1-1
χ61111111111111111-1-1-1-1111111111-1-1-1-1111111-1-111-1-1-1-11-1-111-1-1-1-1-1-1-1-11111-1-111
χ71111111111111111-1-1-1-111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-111
χ81111111111111111-1-1-1-111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-1111111-1-1
χ9111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ10111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ11111111111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111111111-1-111-1-1-11-11
χ12111111111111-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1111111-1-111-1-1111-11-1
χ13111111111111-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1111111-1-1-1-1111-1-11
χ14111111111111-1-1-1-1-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-111-1-11111-1-11111-1-1-111-1
χ15111111111111-1-1-1-1-1-1-1-111-1-1-1-11-1-11111-1-11111-1-1-1-11111-11111-1-1-1-111-1-1-1-111-111-1
χ16111111111111-1-1-1-1-1-1-1-111-1-1-1-11-1-11111-1-11111-1-1-1-11111-11111-1-1-1-1-1-11111-1-11-1-11
χ172222222-222-2222222222-2-20000-2222222-2-20000-2-2000000-2-2-2000000000000000000
χ182222222-222-222222-2-2-2-2-2-20000-222-2-2-2-2-2-2000022000000-222000000000000000000
χ192222222-222-22-2-2-2-22222-2-20000-2-2-2-2-2-2-2220000-2-2000000222000000000000000000
χ202222222-222-22-2-2-2-2-2-2-2-2-2-20000-2-2-22222220000220000002-2-2000000000000000000
χ21222222-22-2-22-2000000002-222-2-2-2002i2i−2i−2i000000002-2000002i−2i002i2i−2i−2i000000000000
χ22222222-22-2-22-2000000002-222-2-2-200−2i−2i2i2i000000002-200000−2i2i00−2i−2i2i2i000000000000
χ23222222-22-2-22-2000000002-2-2-222-2002i2i−2i−2i00000000-22000002i−2i00−2i−2i2i2i000000000000
χ24222222-22-2-22-2000000002-2-2-222-200−2i−2i2i2i00000000-2200000−2i2i002i2i−2i−2i000000000000
χ25222222-2-2-2-2-2-200000000-2200002002i2i−2i−2i002i2i−2i−2i000022-2-20−2i2i2i−2i0000000000000000
χ26222222-2-2-2-2-2-200000000-2200002002i2i−2i−2i00−2i−2i2i2i0000-2-2220−2i2i−2i2i0000000000000000
χ27222222-2-2-2-2-2-200000000-220000200−2i−2i2i2i002i2i−2i−2i0000-2-22202i−2i2i−2i0000000000000000
χ28222222-2-2-2-2-2-200000000-220000200−2i−2i2i2i00−2i−2i2i2i000022-2-202i−2i−2i2i0000000000000000
χ292222-2-222-222-2000022-2-2-2-222-2-220000000000002-2-222-22-2000000000000000000000
χ302222-2-222-222-2000022-2-2-2-2-2-22220000000000002-22-2-22-22000000000000000000000
χ312222-2-222-222-20000-2-222-2-222-2-22000000000000-22-22-22-22000000000000000000000
χ322222-2-222-222-20000-2-222-2-2-2-2222000000000000-222-22-22-2000000000000000000000
χ332222-2-22-2-22-2-2000022-2-2220000-2000000002i2i−2i−2i-22000000000−2i2i2i−2i2i−2i000000000000
χ342222-2-22-2-22-2-2000022-2-2220000-200000000−2i−2i2i2i-220000000002i−2i−2i2i−2i2i000000000000
χ352222-2-22-2-22-2-20000-2-222220000-2000000002i2i−2i−2i2-2000000000−2i2i−2i2i−2i2i000000000000
χ362222-2-22-2-22-2-20000-2-222220000-200000000−2i−2i2i2i2-20000000002i−2i2i−2i2i−2i000000000000
χ372222-2-2-222-22222220000-222222-2-2-2000022222200-2-20000-200-2-20000000000000000
χ382222-2-2-222-22222220000-22-2-2-2-2-2-2-2000022-2-2-2-200220000-200220000000000000000
χ392222-2-2-222-222-2-2-2-20000-222222-2220000-2-2-2-2-2-200-2-20000200220000000000000000
χ402222-2-2-222-222-2-2-2-20000-22-2-2-2-2-2220000-2-2222200220000200-2-20000000000000000
χ412222-2-2-2-22-2-22222200002-200002-2-20000-2-2000000002-2-22200002-2-22000000000000
χ422222-2-2-2-22-2-22222200002-200002-2-20000-2-200000000-222-220000-222-2000000000000
χ432222-2-2-2-22-2-22-2-2-2-200002-20000222000022000000002-2-22-20000-222-2000000000000
χ442222-2-2-2-22-2-22-2-2-2-200002-2000022200002200000000-222-2-200002-2-22000000000000
χ4522-2-22-2-20220-222-2-22-22-200000002-22-22-200000000000000000000000i2−i2i2−i2i2−i2i2−i20000
χ4622-2-22-2-20220-222-2-22-22-200000002-22-22-200000000000000000000000−i2i2−i2i2−i2i2−i2i20000
χ4722-2-22-2-20220-222-2-2-22-2200000002-2-22-2200000000000000000000000i2−i2i2−i2−i2i2−i2i20000
χ4822-2-22-2-20220-222-2-2-22-2200000002-2-22-2200000000000000000000000−i2i2−i2i2i2−i2i2−i20000
χ4922-2-22-2-20220-2-2-2222-22-20000000-22-22-2200000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ5022-2-22-2-20220-2-2-2222-22-20000000-22-22-2200000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ5122-2-22-2-20220-2-2-222-22-220000000-222-22-200000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ5222-2-22-2-20220-2-2-222-22-220000000-222-22-200000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ5344-4-44-440-4-404000000000000000004i−4i−4i4i00000000000000000000000000000000000
χ5444-4-44-440-4-40400000000000000000−4i4i4i−4i00000000000000000000000000000000000
χ5544-4-4-44404-40-444-4-400000000000-44000000000000000000000000000000000000000
χ5644-4-4-44404-40-4-4-444000000000004-4000000000000000000000000000000000000000
χ5744-4-4-44-40-440400004-4-44000000000000000000000000000000000000000000000000
χ5844-4-4-44-40-44040000-444-4000000000000000000000000000000000000000000000000
χ594-44-4000400-4022−2222−22000000004i−4i000000022−222i2−2i22i2−2i200000000000000000000000000000
χ604-44-4000400-4022−2222−2200000000−4i4i000000022−22−2i22i2−2i22i200000000000000000000000000000
χ614-44-4000400-40−2222−2222000000004i−4i0000000−2222−2i22i2−2i22i200000000000000000000000000000
χ624-44-4000400-40−2222−222200000000−4i4i0000000−22222i2−2i22i2−2i200000000000000000000000000000
χ634-44-4000-4004022−2222−220000004-4000000000−222222−22−222200000000000000000000000000000
χ644-44-4000-4004022−2222−22000000-44000000000−2222−222222−2200000000000000000000000000000
χ654-44-4000-40040−2222−22220000004-400000000022−22−222222−2200000000000000000000000000000
χ664-44-4000-40040−2222−2222000000-4400000000022−2222−22−222200000000000000000000000000000
χ678-8-880000000042−42−42420000000000000000000000000000000000000000000000000000
χ688-8-8800000000−424242−420000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).